Many if not most people at this point are paying for one or two always-connected internet connections, in the form of a home connected ISP and a mobile phone. How about everyone runs a small server on their home network and/or cell phone and hosts their profile and personal data, newsfeed contributions etc. from that source.
Maybe am being naive about intrinsic difficulties here, but it seems like the only way to solve this issue is to move away from any reliance on central servers, so no one entity (whether for-profit, non-profit or governmental), controls all the data, and just create a fully P2P network along the lines of the telephone system + some modern web tech. Pretty sure all the pieces to put this together exist already - it’s just a question of whose interest it is in to build that has both motivation and ability.